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  Snakes and ladders in an inhomogeneous neural field model

Avitabile, D., & Schmidt, H. (2015). Snakes and ladders in an inhomogeneous neural field model. Physica D: Nonlinear Phenomena, 294, 24-36. doi:10.1016/j.physd.2014.11.007.

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 Creators:
Avitabile, Daniele1, Author
Schmidt, Helmut1, Author              
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1External Organizations, ou_persistent22              

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Free keywords: Neural fields; Bumps; Localized states; Snakes and ladders; Inhomogeneities
 Abstract: Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic modulation of the synaptic connectivity kernel and find that they are arranged in a snakes-and-ladders bifurcation structure. In the case of Heaviside firing rates, we construct analytically symmetric and asymmetric states and hence derive closed-form expressions for the corresponding bifurcation diagrams. We show that the approach proposed by Beck and co-workers to analyze snaking solutions to the Swift–Hohenberg equation remains valid for the neural field model, even though the corresponding spatial–dynamical formulation is non-autonomous. We investigate how the modulation amplitude affects the bifurcation structure and compare numerical calculations for steep sigmoidal firing rates with analytic predictions valid in the Heaviside limit.

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Language(s): eng - English
 Dates: 2014-11-262014-03-062014-11-272015-02-152015-02-15
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1016/j.physd.2014.11.007
 Degree: -

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Title: Physica D: Nonlinear Phenomena
  Other : Physica D
Source Genre: Journal
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Publ. Info: Amsterdam : North-Holland
Pages: - Volume / Issue: 294 Sequence Number: - Start / End Page: 24 - 36 Identifier: ISSN: 0167-2789
CoNE: https://pure.mpg.de/cone/journals/resource/954925482641